By making effects explicit, you reap the benefit of being able to write non-effectful code.

Depending on what your language tracked as an effect, you could make your business-logic always terminate, or perform no allocations, if you had effects for Mutation/GeneralRecursion/Allocation.

But no, I certainly don't understand the function->handler control flow here. It has to be handler->function, otherwise you've got two handlers!

a function will return to it's call site (or diverge), a handler doesn't necessarily have to resume from where it was invoked. There is also (sort of) dynamic scoping, where you don't have to thread the handlers through calls.